北京邮电大学高等数学第一册答案
北京邮电大学双语高等数学教学组 2011 年第一版?
1.1 Part?A?
1. (1) A ∪ B = {1, 2,3, 4,5, 6, 7,8} , A ∩ B = {8} , A \ B = {1,3,5, 7} , B \ A = {2, 4, 6} . (2) A ∪ B = {all parallelograms} , A ∩ B = {all rectangles} , A \ B = {all parallelograms except rectangles} , B \ A = ? . (3) A ∪ B = {1, 2,3, 2. . ∩ Aic = {5, 9} .
i =1 5
},
A ∩ B = {2, 4, 6,
},
A \ B = {1,3,5,
},
B \ A = ?.
3.
A ∪ B = {1 < x ≤ 3} A ∩ B = ? .
1? ? ? ?∞, ? . 2? ?
5. (1)
(2) (α , β ) ∪ ( γ , +∞ ) .
π 2π ? ? (3) ? 2kπ + , 2kπ + . 3 3 ? ? ?
(4)
( 0, +∞ ) .(5) ( ?4, ?2 ) .(6) ( ?3, ?2] . (1, +∞ ) .
2 ? (7) (1, 2 ) ∪ ( 2, 4] . (8) ? ? ,1? . (9) ? 2 ?
磐安
玻璃栈道
( 0, +∞ ) .
(10) [ 0, 2 ) .
(11)
6.
1 ? ? a ≤ x ≤ 1 ? a, 0 < a ≤ 2 ? . (1) [ ?1, 0] .(2) [ 0,1] .(3) ? 2kπ , ( 2k + 1) π ? , k ∈ Z .(4) ? ? ? ?? , a > 1 ? 2 ?
7. (1) No. (2) No.(3) 8. (1) Yes.(2) Yes.(3)
No. (4)Yes.(5) No. (6) Yes.(7) No. (8)Yes.(9) No. (10) Yes. Yes.
5 ? 3x, x < 1 ? 11. f ( x ) = ?3 ? x, 1 ≤ x < 2 . ?3x ? 5 x ≥ 2 ?
12. (1) y = u 3 , u = sin v , v = w and w = 1 ? 2 x .(2) y = arccos u , u =
x?2 1 .(3) y = , u = 1 + v , v = arctan w , w = 2 x . u 2
(4) y = u10 , u = 1 + 2 x .(5) y = u 2 , u = arcsin v , v = x 2 .(6) y = ln (1 + u ) , u = 1 + v , v = x 2 .(7) y = 2u , u = v 3 , v = sin x . 13.
( f φ )( x ) = sin 3 2 x ? sin 2 x,
x ∈ ( ?∞, +∞ ) , (φ f )( x ) = sin 2 ( x 3 ? x ) ,
x ∈ ( ?∞, +∞ ) ,
(f
f )( x ) = x ? 2 x3 + 3x5 ? 3x 7 + x9 , x ∈ ( ?∞, +∞ ) .
1/ e, | x |< 1 ? ( g f )( x ) = ?1, | x |= 1 ?e, | x |> 1 ?
1, x < 0 ? 14. ( f g )( x ) = ?0, x = 0 ?1, x>0 ?
Advanced?Mathematics
School?of?Science,?BUPT?
Oct.?2011?
北京邮电大学双语高等数学教学组 2011 年第一版?
0, x >1 ? 15. f ( x ) = ?h ( x + 1) , ?1 ≤ x < 0 ?? h ( x ? 1) , 0 ≤ x ≤ 1 ?
0, x < ?1 ? ? g ( x ) = ? 1 ? x2 , ?1 ≤ x ≤ 1 . ? ? 3 ( x ? 1) , x > 1 ? 3 ? 1 y x = e y ?1 ? 2 .(3) x = arcsin , 3 2
17. (1) x = ? 1 ? y 2 ,
2
( 0 ≤ y ≤ 1) .(2)
( ?2 ≤ y ≤ 2 ) .(4)
x = log 3
(1 ? y )
y
,
y +1? ?∞ < y < 1 ? y, ? ? ?1 ? ? 1? y ? 1≤ y ≤ 2 . (5) x = y ∈ [ ?1,1) .(6) x = ? y , 2 ?log y, 2 < y < +∞ ? 2
Part?B?
1. (1)
(f
g )( x ) = 0,
( x = 0) , ( g
f )( x ) = 2 ? x 2 ,
(1 ≤ x ≤ 2 ) .
x ? (2) ( f g )( x ) = arcsin ? ? 1? , ?2 ? 1 ? 2 x 2 + 2 x3 , ?1 + x
1 0 ≤ x ≤1 ? 2 arcsin ( x ? 1) , ? . ( 0 ≤ x ≤ 4 ) , ( g f )( x ) = ? ? 2 ? ? 1 arcsin ? x ? 1 ? , 1 < x ≤ 2 ?2 ? 2 ? ?
2.
f ( x) =
( ?∞ < x < 0 ) .
3.
x + 1, x ∈ ( ?1, 0] ? f ?1 ( x ) = ? x ∈ [1, 2] ? x ? 1, ?
6. 8.
f ( x) = x +1 .
1? ? 1? 1 ? f ( x ) = x2 ? 2 . f ? x ? ? = ? x ? ? ? 2 = x 2 + 2 ? 4 . x? ? x? x ?
2
1.2 Part?A?
1. (1) No. (2) Yes. (3) Yes,.(4) No. 2. (1) wrong.(2) wrong(3) wrong.. 5. wrong 6. wrong
1 9. (1) . 2
1 (2) . 3
(3) 2 . (4) 2 .
(5)
1 . 3
(6)
1 . e
Advanced?Mathematics
School?of?Science,?BUPT?
Oct.?2011?
北京邮电大学双语高等数学教学组 2011 年第一版?
0, l m ?
l l ?1
13. (1) convergent. (2) divergent. (3) convergent.
1.3 Part?A?
1. (1) ?ε >0 , ?X > 0 ,
f ( x ) ? A < ε holds for all x > X . (2) ?ε > 0 , ?δ > 0 ,
f ( x ) ? A < ε holds for all x0 ? x < δ .
(3) ?M < 0 , ?δ > 0 , f ( x ) < M holds for all x ? 2 < δ . 2. (1) wrong. (2) right. 3. (1) wrong. (2) right. (2) right. (2) wrong. (2)wrong. (2) wrong. (7) Yes. (8) No.
5. (1) No. (2) No. (3) No. (4) No. (5) No. (6) No. 6. (1) ?3 7. (1)
1 2
1 4
(3) 1 (3) ?1
(4) 3 (4)
1 2
(5)大连老虎滩渔人码头
33 4 (6) cos x (7) ? sin x (8) 0 2
2
π
(5) e ?6
比利时vs巴西(6) e ?2
(7) π
(8) e 2
8. (1) a = ?1 b = ?2
(2) a =
Part?B?
1. (1)
4 3
(2) e ?2
(3) e ?1/ 2
2
(4) e π
济南蟠龙山滑雪场f ( x ) ? A > ε holds for all x ∈ U ( x0 , δ ) .
3. some ε > 0 , there exists a δ > 0 , such that
2
4.
eπ
1.4 Part?A?
